SRC/dsbtrd.f(3)

NAME
SRC/dsbtrd.f

SYNOPSIS

  Functions/Subroutines
subroutine dsbtrd (vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)
DSBTRD

Function/Subroutine Documentation

  subroutine dsbtrd (character vect, character uplo, integer n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldq, * ) q, integer ldq, double precision, dimension( * ) work, integer info)

DSBTRD

Purpose:

    !>
    !> DSBTRD reduces a real symmetric band matrix A to symmetric
    !> tridiagonal form T by an orthogonal similarity transformation:
    !> Q**T * A * Q = T.
    !>

Parameters
    VECT

    !>          VECT is CHARACTER*1
    !>          = 'N':  do not form Q;
    !>          = 'V':  form Q;
    !>          = 'U':  update a matrix X, by forming X*Q.
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    KD

    !>          KD is INTEGER
    !>          The number of superdiagonals of the matrix A if UPLO = 'U',
    !>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
    !>

    AB

    !>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
    !>          On entry, the upper or lower triangle of the symmetric band
    !>          matrix A, stored in the first KD+1 rows of the array.  The
    !>          j-th column of A is stored in the j-th column of the array AB
    !>          as follows:
    !>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    !>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
    !>          On exit, the diagonal elements of AB are overwritten by the
    !>          diagonal elements of the tridiagonal matrix T; if KD > 0, the
    !>          elements on the first superdiagonal (if UPLO = 'U') or the
    !>          first subdiagonal (if UPLO = 'L') are overwritten by the
    !>          off-diagonal elements of T; the rest of AB is overwritten by
    !>          values generated during the reduction.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= KD+1.
    !>

    D

    !>          D is DOUBLE PRECISION array, dimension (N)
    !>          The diagonal elements of the tridiagonal matrix T.
    !>

    E

    !>          E is DOUBLE PRECISION array, dimension (N-1)
    !>          The off-diagonal elements of the tridiagonal matrix T:
    !>          E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.
    !>

    Q

    !>          Q is DOUBLE PRECISION array, dimension (LDQ,N)
    !>          On entry, if VECT = 'U', then Q must contain an N-by-N
    !>          matrix X; if VECT = 'N' or 'V', then Q need not be set.
    !>
    !>          On exit:
    !>          if VECT = 'V', Q contains the N-by-N orthogonal matrix Q;
    !>          if VECT = 'U', Q contains the product X*Q;
    !>          if VECT = 'N', the array Q is not referenced.
    !>

    LDQ

    !>          LDQ is INTEGER
    !>          The leading dimension of the array Q.
    !>          LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  Modified by Linda Kaufman, Bell Labs.
    !>

Definition at line 161 of file dsbtrd.f.

Author

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